In the prior art, previous efforts have been made to produce female urinary collection devices. One example is disclosed in the Hall and Beecher U.S. Pat. No. 4,496,355, issued Jan. 29, 1985, and entitled EXTERNAL FEMALE URINARY APPLIANCE. Such appliance includes a generally cup-shaped receptacle which is Worn by the female user so as to enclose the external orifice of the urethra. Such prior appliance has various disadvantages and problems, in that such appliance is somewhat uncomfortable to wear, and is subject to leakage of urine in some cases, due in large part to the fact that such appliance is unable to accommodate itself to the rather considerable variations in the shape of different female bodies, around the orifice of the urethra. If the pressure between such prior appliance and the female body is increased to reduce the incidence of leakage, the discomfort to the wearer is increased. Such prior appliance involves the further problem that the appliance is subject to dislocation from its intended position, in sealing engagement with the female body around the orifice of the urethra.